You know the 100 coolest Americans must be a pretty hip bunch if Janis Joplin, Chet Baker, Dean Martin and George Clooney fail to make the cut.

Elvis Presley, James Dean, Bruce Springsteen and Madonna do make the choice of a hundred actors, actresses, artists, musicians and writers in the United States whose creativity and style have shaped the concept of cool. There is even a welcome place for country singer Willie Nelson in the exhibition at the National Portrait Gallery in Washington.

The exhibition, which took five years to bring to fruition, has been put together by Joel Dinerstein, professor of American Civilisation at Tulane University in New Orleans, and Frank Goodyear III, co-director of Bowdoin College Museum of Art.

To make their selection, the two curators came up with four defining factors of cool, of which people chosen had to fit at least three categories:

Another deciding factor was that there had to be a good picture of the person and among the photographers featured in the show are Diane Arbus, Annie Leibovitz, Robert Mapplethorpe, Edward Steichen and Herman Leonard.

A museum-goer looks at a photograph of Bruce Springsteen by Annie Leibovitz, one of the 100 stars in the 'American Cool' exhibition at the National Portrait Gallery in Washington AFP/GETTY IMAGES

Dinerstein, who is also an advisor on the HBO show Boardwalk Empire, is a jazz expert, and musicians are well represented in the list, starting from Bix Beiderbecke and Bessie Smith in 'The Roots of Cool' section to legends such as Miles Davis. Dinerstein said: "It was in the Forties and Fifties that cool was truly born, with jazz legends like Miles Davis, Duke Ellington, Dizzy Gillespie, Billie Holiday, Thelonious Monk, Charlie Parker and Lester Young coming to the fore." Dinerstein credits jazz saxophonist Young with coining the use of the term 'cool'.

"Cool is America's greatest cultural export," said Australian Kim Sajet, who took over last year as director of the National Portrait Gallery, which is part of the Smithsonian network of museums.

The list opens with 19th-century poet Walt Whitman, author of Leaves of Grass, who is described as “the guiding light of American bohemia” and includes modern culture figures such as Jay-Z and Quentin Tarantino. Dinerstein said: "There are people on this list who I wish were not, but our culture has elevated them to cool. My example is Quentin Tarantino. I don’t like his films and I don’t like him. But there’s no question of his national and global influence both on art and film and everyone under 40."

A poster-sized still from the 1969 road movie Easy Rider at the American Cool exhibition AFP/GETTY IMAGES

Just under a quarter of the 100 are women – including Madonna, Mae West and Bonnie Raitt – and includes, bizarrely, some non-Americans (such as Canadian-born Neil Young and Belgian-born Audrey Hepburn).

People will obviously disagree with the choices – Sidney Poitier, Slim Gaillard, Louis Armstrong, Groucho Marx could all have been in the 100 – and the curators have tried to mollify critics by doing an 'Alt 100' list of also-rans that includes, for example, Sam Cooke, Janis Joplin and Stan Getz.

American Cool is accompanied by a fully illustrated 192-page catalogue of the same title, published by Delmonico Books.